Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique |
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Authors: | Guy Henniart |
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Institution: | (1) Département de Mathématiques, UMR 8628 du CNRS, bat. 425, Université de Paris-Sud, F-91405 Orsay Cedex, France (e-mail: Guy.Henniart@math.u-psud.fr), FR |
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Abstract: | Let F be a finite extension of ℚ
p
. For each integer n≥1, we construct a bijection from the set ?F
0
(n) of isomorphism classes of irreducible degree n representations of the (absolute) Weil group of F, onto the set ?
F
0
(n) of isomorphism classes of smooth irreducible supercuspidal representations of GL
n
(F). Those bijections preserve epsilon factors for pairs and hence we obtain a proof of the Langlands conjectures for GL
n
over F, which is more direct than Harris and Taylor’s. Our approach is global, and analogous to the derivation of local class field
theory from global class field theory. We start with a result of Kottwitz and Clozel on the good reduction of some Shimura
varieties and we use a trick of Harris, who constructs non-Galois automorphic induction in certain cases.
Oblatum 1-III-1999 & 21-VII-1999 / Published online: 29 November 1999 |
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Keywords: | Mathematics Subject Classification (1991): 11F70 11R39 11S37 22E50 22E55 |
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